In a game dripping with tension between two evenly matched teams that had 17 lead changes and was tied a dozen times, young Alexey Shved caught fire from the outside to lead the Russians to victory.
"How sweet it is," said Russia coach David Blatt.
Russia used a third-quarter hot streak to take an 11-point lead but Argentina closed the quarter with seven straight points to make it 61-57.
Shved, 23, scored seven points in a row for Russia to snap a 64-64 deadlock and lift them to a 71-66 fourth-quarter lead.
A pair of three-pointers for Argentina by Andres Nocioni and Manu Ginobili tied the game 72-72 and a twisting, left-handed reverse layup by Ginobili gave the Argentines a 77-76 lead and the inside track for the medal with 44 seconds left.
Shved then stepped up and drilled a three-pointer to put Russia ahead 79-77 and after a three-point try from the corner by Nocioni rattled around the rim and out, a fastbreak layup by Vitaliy Fridzon completed the scoring.
"I played two games bad but the third game is my game," said Shved, a long-haired guard who struggled with his consistency in the tournament.
"It is one of the best moments in my life. When you come to an Olympic Games and win a medal - not every athlete can do this."
Andrei Kirilenko, the veteran forward and leader of the team, was excited about Russia's return to the podium for the first time since taking bronze at the Sydney Games in 2000.
"I feel like it's a gold medal," he said. "I think we did a very good job today. In the second half when we fell down we stayed together to get that win."
At the buzzer, the Russians collapsed one after another into a heap at the top of the key to celebrate.
Shved led all scorers with 25 points, 13 of them coming in the pressure-packed fourth quarter, with former NBA All-Star Kirilenko adding 20 and Fridzon contributing 19 points.
Ginobili, with 21 points, was top scorer for Argentina, whose medals streak was snapped after claiming gold in 2004 and bronze in 2008.
"It was a very tough game. It could've gone for either one," said Ginobili. "In the last seconds anything can happen. At the end their shots went in and ours went in and out."